Forested Skorpios is where Aristotle Onassis married Jackie Kennedy in 1968. He is buried there, alongside his son Alexander and daughter Christina, the mother of Athina.

An outright sale of the island is "almost impossible" under the terms of Aristotle Onassis' will, the mayor said.

Swiss-born Athina Roussel Onassis, 28, is married to the Brazilian equestrian champion Alvaro Alfonso de Miranda Neto and lives for the most part in Brazil.

"She has not been to the island for years," Zavitsanos said, placing her last visit around 2004.

When Onassis turned 18, her inheritance was believed to include mansions in Paris, Geneva and the Spanish island of Ibiza, an art collection including works by French sculptor Auguste Rodin and impressionist paintings, a sizeable share portfolio, jewellery and luxury cars.

It is estimated to be worth half of Aristotle Onassis' fortune.

The remainder, including shipping operations, is administered by the Onassis Foundation, which the tycoon set up before his death.

The foundation declined to comment on the issue on Friday.

The owners of several private Greek islands have been trying to offload their property in recent months owing to the country's economic crisis and a related real-estate tax crackdown by the government.

Last month, Greek media reported that the emir of Qatar had purchased a group of Ionian Sea islets for 8.8 million euros ($11.5 million).